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The aim of this work is to study the characteristics of tinnitus both in normal hearing subjects and in patients with hearing loss. The study considered tinnitus sufferers, ranging from 21 to 83 years of age, who were referred to the Audiology Section of Palermo University in the years 2006-2008. The following parameters were considered: age, sex, hearing threshold, tinnitus laterality, tinnitus duration, tinnitus measurements and subjective disturbance caused by tinnitus. The sample was divided into Group1 (G1), 115 subjects with normal hearing, and Group2 (G2), 197 subjects with hearing loss. Especially for G2, there was a predominance of males compared to females (P = 0.011); the highest percentage of tinnitus resulted in the decades 61-70 and >70 with a significant difference for G2 demonstrating that the hearing status and the elderly represent the principal tinnitus-related factors (P < 0.0001). The hearing impairment resulted in most cases of sensorineural hearing loss (SNHL) type and was limited to the high frequencies; the 72.1% of the patients with SNHL had a high-pitched tinnitus, while the 88.4% of the patients with a high-frequency SNHL had a high-pitched tinnitus (P < 0.0001). As to the subjective discomfort, the catastrophic category was the most representative among G1 with a significant difference between the two groups; no correlation was found between the level of tinnitus intensity and the tinnitus annoyance confirming the possibility that tinnitus discomfort is elicited by a certain degree of psychological distress as anxiety, depression, irritability and phobias.

In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.

We consider Prandtl's equations for the impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen's singularity as a cubic root singularity.We introduce a class of initial data which have a dipole singularity in the complex plane. These data are uniformly bounded in H 1 and lead to an earlier singularity formation. The presence of a small viscosity in the streamwise direction changes the behavior of the singularities.

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Numerical solutions of the laminar Prandtl boundary-layer and NavierStokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and NavierStokes solutions and analyze the previous interactions from a different perspective.

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